Chapter 3 Pair of Linear Equations in Two Variables- MCQ Online Test 2 Class 10 Maths
1.The solution of px + qy = p – q and qx – py = p + q is
x = 1 and y = – 1
x = – 1 and y = 1
x = 0 and y = 0
x = 1 and y = 1
2. The value of ‘a’ so that the point (3, a) lies on the line represented by 2x – 3y = 5 is
-1/3
-1
1
1/3
3. If (x + 1) is a factor of 2x³ + ax² + 2bx + 1, then find the values of ‘a’ and ‘b’, given that 2a – 3b = 4
a = 5 and b = 2
a = – 5 and b = – 2
a = 5 and b = – 2
a = – 5 and b = 2
4. The lines representing the pair of equations 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0
are parallel
none of these
intersect at a point
are coincident
5. The angles of a triangle arex°, y° and 40°. The difference between the two angles ‘x’ and ‘y’ is 30°, then
x°= 85° and y°= 55°
x° = 75° and y° = 45°
none of these
x°= 65° and y° = 95°
6. 5 pencils and 7 pens together cost Rs.50 whereas 7 pencils and 5 pens together cost Rs.46. The cost of 1 pen is
Rs.6
Rs.3
Rs.4
Rs.5
7. The lines representing the pair of equations 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0
are parallel
intersected at two points
are coincident
intersect at a point
8. The lines representing the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0
are coincident
are parallel
Intersect at a point
Intersected at two points
9. The system of equations x – 4y = 8, 3x – 12y = 24
may or may not have a solution
has no solution
has infinitely many solutions
has a unique solution
10. The sum of the digits of a two digit number is 9. Nine times this number is twice the number obtained by reversing the digits, then the number is
27
72
18
81
Chapter - 3 A Pair of Linear Equation in two Variables Quiz - 2 Class - 10th
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Question 1 of 10
The solution of px + qy = p – q and qx – py = p + q is
Correct
Incorrect
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Question 2 of 10
The value of ‘a’ so that the point (3, a) lies on the line represented by 2x – 3y = 5 is
Correct
Explanation
2x−3y=5
⇒ 2×3−3×a=5
⇒ 6−3a=5
⇒ a = 1/3
Incorrect
Explanation
2x−3y=5
⇒ 2×3−3×a=5
⇒ 6−3a=5
⇒ a = 1/3
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Question 3 of 10
If (x + 1) is a factor of 2x³ + ax² + 2bx + 1, then find the values of ‘a’ and ‘b’, given that 2a – 3b = 4
Correct
Explanation:
Given that (x+1) is a factor of p(x)
therefore, -1 is a zero of given p(x)
p(x) = 2x3 +ax2 +2bx + 1
Substituting the value of -1 in the given p(x),we get
p(x) = 2 × (-1)3 + a × (-1)2 + 2×b× (-1) + 1
= -2 + a -2b + 1
= -1 + a – 2b
or, a – 2b = 1
Also, given that 2a – 3b = 4
So we get two equations;
a – 2b = 1 …(1)
2a – 3b = 4 …(2)
Multiplying eqn.1 with 2, we get
2a – 4b = 2 …(3)
Subtracting eqn. 3 from eqn. 2
[ 2a – 2a ] + [ -3b – (-4b) ] = 4-2
⇒ -3b + 4b = 2
therefor, b=2
Substituting the value of b in eqn.(3)
2a – 4b = 2
⇒ 2a – (4×2) = 2
⇒ 2a – 8 = 2
⇒ 2a = 2 + 8
⇒ 2a = 10
⇒ a = 10/2
therefore, a = 5
Thus, a =5 and b=2
Incorrect
Explanation:
Given that (x+1) is a factor of p(x)
therefore, -1 is a zero of given p(x)
p(x) = 2x3 +ax2 +2bx + 1
Substituting the value of -1 in the given p(x),we get
p(x) = 2 × (-1)3 + a × (-1)2 + 2×b× (-1) + 1
= -2 + a -2b + 1
= -1 + a – 2b
or, a – 2b = 1
Also, given that 2a – 3b = 4
So we get two equations;
a – 2b = 1 …(1)
2a – 3b = 4 …(2)
Multiplying eqn.1 with 2, we get
2a – 4b = 2 …(3)
Subtracting eqn. 3 from eqn. 2
[ 2a – 2a ] + [ -3b – (-4b) ] = 4-2
⇒ -3b + 4b = 2
therefor, b=2
Substituting the value of b in eqn.(3)
2a – 4b = 2
⇒ 2a – (4×2) = 2
⇒ 2a – 8 = 2
⇒ 2a = 2 + 8
⇒ 2a = 10
⇒ a = 10/2
therefore, a = 5
Thus, a =5 and b=2
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Question 4 of 10
The lines representing the pair of equations 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0
Correct
Given : pair of equations 5x – 4y + 8 =0 and 7x + 6y -9 = 0
To Find : The lines representing the pair are parallel , coincident , Intersect at a point or none of these
Solution:
Two lines
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
parallel if a₁/a₂ = b₁/b₂
Coincident if a₁/a₂ = b₁/b₂ = c₁ / c₂
Intersect at a point if a₁/a₂ ≠ b₁/b₂
Lets check for
5x – 4y + 8 =0
7x + 6y -9 = 0
a₁/a₂ = 5/7
b₁/b₂ = – 4/6
c₁/c₂ = 8/-9
5/7 ≠ – 4/6
a₁/a₂ ≠ b₁/b₂
⇒ lines intersect at a point
Additional info:
15x – 12y + 24 + 14x + 12y – 18 = 0
⇒ 29x = -6
⇒ x = -6/29
35x – 28y + 56 = 35x + 30y – 45
⇒ 58y = 101
⇒ y = 101/58
intersection point ( -6/29 , 101/58)
5x – 4y + 8 =0 and 7x + 6y -9 = 0 lines intersect at a point
Incorrect
Given : pair of equations 5x – 4y + 8 =0 and 7x + 6y -9 = 0
To Find : The lines representing the pair are parallel , coincident , Intersect at a point or none of these
Solution:
Two lines
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
parallel if a₁/a₂ = b₁/b₂
Coincident if a₁/a₂ = b₁/b₂ = c₁ / c₂
Intersect at a point if a₁/a₂ ≠ b₁/b₂
Lets check for
5x – 4y + 8 =0
7x + 6y -9 = 0
a₁/a₂ = 5/7
b₁/b₂ = – 4/6
c₁/c₂ = 8/-9
5/7 ≠ – 4/6
a₁/a₂ ≠ b₁/b₂
⇒ lines intersect at a point
Additional info:
15x – 12y + 24 + 14x + 12y – 18 = 0
⇒ 29x = -6
⇒ x = -6/29
35x – 28y + 56 = 35x + 30y – 45
⇒ 58y = 101
⇒ y = 101/58
intersection point ( -6/29 , 101/58)
5x – 4y + 8 =0 and 7x + 6y -9 = 0 lines intersect at a point
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Question 5 of 10
The angles of a triangle arex°, y° and 40°. The difference between the two angles ‘x’ and ‘y’ is 30°, then
Correct
Incorrect
-
Question 6 of 10
5 pencils and 7 pens together cost Rs.50 whereas 7 pencils and 5 pens together cost Rs.46. The cost of 1 pen is
Correct
Explanation:
Let the cost of one pencil = x
Cost of one pen = y
According to question,
5x+7y = 50 …….. (1)
7x + 5y = 46 ………(2)
Multiply equation 1 by 7 and equation 2 by 5 we get
7(5x+7y)= 7×50
⇒ 35x +49y = 350 …….(3)
and
5(7x +5y) = 5×46
⇒ 35x +25y = 230 ……. (4)
Subtracting equation 4 from equation 3 , we get
35x + 49y – 35x – 25y = 350 -230
⇒ 49y -25y = 120
⇒ 24y = 120
⇒ y = 120 /24
⇒ y= 5
Substitute y=5 in equation 1 , we get
5x + 7×5 =50
⇒ 5x+35 =50
⇒ 5x = 50 – 35
⇒ 5x =15
⇒ x= 15/5
⇒ x=3
Hence Cost of One Pen =y =5
Incorrect
Explanation:
Let the cost of one pencil = x
Cost of one pen = y
According to question,
5x+7y = 50 …….. (1)
7x + 5y = 46 ………(2)
Multiply equation 1 by 7 and equation 2 by 5 we get
7(5x+7y)= 7×50
⇒ 35x +49y = 350 …….(3)
and
5(7x +5y) = 5×46
⇒ 35x +25y = 230 ……. (4)
Subtracting equation 4 from equation 3 , we get
35x + 49y – 35x – 25y = 350 -230
⇒ 49y -25y = 120
⇒ 24y = 120
⇒ y = 120 /24
⇒ y= 5
Substitute y=5 in equation 1 , we get
5x + 7×5 =50
⇒ 5x+35 =50
⇒ 5x = 50 – 35
⇒ 5x =15
⇒ x= 15/5
⇒ x=3
Hence Cost of One Pen =y =5
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Question 7 of 10
The lines representing the pair of equations 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0
Correct
Incorrect
-
Question 8 of 10
The lines representing the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0
Correct
Incorrect
-
Question 9 of 10
The system of equations x – 4y = 8, 3x – 12y = 24
Correct
Incorrect
-
Question 10 of 10
The sum of the digits of a two digit number is 9. Nine times this number is twice the number obtained by reversing the digits, then the number is
Correct
Explanation:
Let unit digit = x Tens digit = y
Original number = 10y+x.
Sum of digits are 9 So that x + y = 9 ………….(1)
According to question,
9 (10y + x) = 2 (10x + y)
⇒ 90y + 9 x = 20x + 2y
⇒ 88y – 11 x = 0
Dividing by 11, we get
8y – x = 0 …………..(2)
Adding equations 1 and 2 , we get
9 y = 9
⇒ y = 9/9 = 1
Putting this value in equation 1 we get
x + y = 9
⇒ x + 1 = 9
⇒ x = 8
Therefore the number is 10(1)+8 = 18
Incorrect
Explanation:
Let unit digit = x Tens digit = y
Original number = 10y+x.
Sum of digits are 9 So that x + y = 9 ………….(1)
According to question,
9 (10y + x) = 2 (10x + y)
⇒ 90y + 9 x = 20x + 2y
⇒ 88y – 11 x = 0
Dividing by 11, we get
8y – x = 0 …………..(2)
Adding equations 1 and 2 , we get
9 y = 9
⇒ y = 9/9 = 1
Putting this value in equation 1 we get
x + y = 9
⇒ x + 1 = 9
⇒ x = 8
Therefore the number is 10(1)+8 = 18
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